Pair creation of nodal lines carrying Z₂ monopole charge (monopole nodal lines) via a double band inversion (DBI). (a) Evolution of band structure during DBI. Red (orange) points and lines indicate the crossing between the conduction and valence bands (two occupied bands). (b) Saddle-shaped band structure when 0 < M < |m|. (c) Change in nodal line structure when two saddle-shaped bands cross. Figures are adopted from the supplemental materials in Ref. [7].